3x+2y=7

Question

2x-3y=-4

Answer 1

Multiply both sides of first equation by 2

6 x + 4 y = 14

Multiply both sides of second equation by 3

6 x - 9 y = - 12

6 x + 4 y = 14
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6 x - 9 y = - 12
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0 + 4 y - ( - 9 y ) = 14 - ( -12 )

4y + 9 y = 14 + 12

13 y = 26

Divide both sides by 13

y = 2

Replace y with 2 in first equation:

3 x + 2 ∙ 2 = 7

3 x + 4 = 7

Subtract 4 to both sides

3 x = 3

x = 1

Or replace y with 2 in second equation:

2 x - 3 ∙ 2 = - 4

2 x - 6 = - 4

Add 6 to both sides

2 x = 2

x = 1

The solution is x = 1 , y = 2

You can write the solution as ( 1 , 2 )